Comparing FEM, BEM and analytical formulations in the evaluation of the stress intensity factor in LEFM

The determination of the stress intensity factor (K), in Linear Elastic Fracture Mechanics (LEFM), is very useful for the investigation of crack propagation of pipelines and pressure vessels. K is related to parameters such as Crack Opening Displacement and J-Integral, among others. The experimental determination of K is expensive and very time consuming. A fast and economical alternative for the determination of K is the use of numerical methods. The Finite Element Method (FEM) and the Boundary Element Method (BEM) are gradually being incorporated into numerical schemes for the determination of K. However, stress gradients, in the area close to the crack tip, are very difficult to be represented. The fundamental solutions of the BEM provide good precision in the calculation of stresses in such areas of high stress gradients. But for both, FEM and BEM, applied to Fracture Mechanics, it is common to use special elements, called 'quarter-point' elements, in the determination of K. Such special elements are employed in FEM and in BEM to represent the singularities idealized at the crack tip. This work presents several determinations of K using the FEM and BEM with common elements without singularity, and with special elements with singularity at the tip of the crack. In the BEM formulation, implicit differentiation of the fundamental solutions for the calculation of J-integral is employed. It is noticed that the singularities at the tip of the crack are mathematical idealizations and maybe are not very important for the calculation of K in practical engineering. This issue is discussed in this article. Several classic examples for the determination of K are presented and the results compared to values available in the literature. (authors)